How to attach sprocket from gum ball machine to a shaft/motor?

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I would like to motorize a gumball hopper to dispense wooden balls for a project. The gumball hopper normally moves the sorting wheel via a gear which is turned by the coin-op handle on the front of the machine (see e.g. here).
I know I can attach a motor to a shaft with a standard coupler (see e.g. here), however I am having trouble seeing how to correctly attach the gear/sprocket to the shaft. I guess I could use a long screw going through the sprocket and into another coupler and just using friction to fix the screw to the sprocket, but that does not seem like a reliable or efficient way of transferring the rotational energy of the shaft to the sprocket.
The sprocket does not have a set screw hole to be fixed to a shaft.
Feel like I must be missing something! The part was originally screwed directly onto another metal part with a form-fitting square peg going into the sprocket's socket.
Let me know if more information would be useful.

Also if I am better off just using a separate made-to-order sprocket, that is fine too!

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You have too many gears and sprockets and shafts there for me to keep track of. There are many ways to attach stuff to stuff. But first do you intend to ever disassemble any of it. That is the key to how you do such things. Second, do you have a shop so you can modify things to make such attachments?

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